A method of replacing the first dispersion medium of a raw slurry composed of a first dispersion medium and crystal terephthalic acid with a second dispersion medium. The raw slurry is fed to a vertically extending cylindrical part of cyclone-shaped nozzle disposed in a superior portion of replacement vessel of dispersion medium replacing apparatus from its tangential direction and undergoes circular motion along the inner wall surface of the cylindrical part. The raw slurry in circular motion is discharged from an opening disposed in a vertically inferior portion of the cylindrical part and dispersed in a second dispersion medium fed from an inferior portion of the replacement vessel. The slurry after replacement composed mainly of crystal terephthalic acid and the second dispersion medium is drawn out from the inferior portion of the replacement vessel, while the first dispersion medium is drawn out from the superior portion of the replacement vessel.